Subgroups — C₇₃×#33788 #32943192

Order 18688.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3155	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2211	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2207	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2189	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2187	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
13	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
15	#541×C₇₃	—	2	1	no	—
16	#535×C₇₃	—	2	1	no	—
17	C₂×Q₃₂×C₇₃	C₂²	1	2	yes	complemented
18	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	—
19	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	—
20	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	complemented
21	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#496×C₇₃	—	2	1	no	—
23	#496×C₇₃	—	2	1	no	—
24	#495×C₇₃	C₂²	1	1	yes	characteristic
25	#495×C₇₃	C₂²	1	1	yes	characteristic
26	#494×C₇₃	C₂²	1	1	yes	characteristic, complemented
27	#493×C₇₃	C₂²	1	1	yes	characteristic
28	#493×C₇₃	C₂²	1	1	yes	characteristic
29	#491×C₇₃	—	2	1	no	—
30	#470×C₇₃	—	2	1	no	—
31	#467×C₇₃	C₂²	1	2	yes	—
32	#441×C₇₃	—	2	1	no	—
33	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
34	#405×C₇₃	C₂²	1	1	yes	characteristic
35	C₄⋊C₁₆×C₇₃	C₂²	1	2	yes	complemented
36	#358×C₇₃	C₂²	1	2	yes	complemented
37	#357×C₇₃	C₂²	1	2	yes	—
38	#357×C₇₃	C₂²	1	2	yes	—
39	#357×C₇₃	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₇₃	C₂²	1	2	yes	—
41	#346×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	—	2	1	no	—
45	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
46	#135×C₇₃	—	4	2	no	—
47	C₂×Q₁₆×C₇₃	—	2	1	no	—
48	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
50	C₂×SD₁₆×C₇₃	—	2	1	no	—
51	C₂×SD₁₆×C₇₃	—	2	1	no	—
52	C₂×SD₁₆×C₇₃	—	2	1	no	—
53	C₂×D₈×C₇₃	—	2	1	no	—
54	C₂×D₈×C₇₃	—	2	1	no	—
55	C₂×D₈×C₇₃	—	2	1	no	—
56	C₂×D₈×C₇₃	—	4	2	no	—
57	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
58	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
59	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₇₃	—	2	1	no	—
63	#127×C₇₃	—	2	1	no	—
64	#127×C₇₃	—	2	1	no	—
65	#126×C₇₃	—	4	2	no	—
66	#125×C₇₃	—	2	1	no	—
67	#125×C₇₃	—	4	2	no	—
68	#124×C₇₃	—	2	1	no	—
69	#124×C₇₃	—	2	1	no	—
70	C₂²⋊Q₈×C₇₃	—	2	2	no	—
71	#121×C₇₃	—	4	2	no	—
72	#120×C₇₃	—	4	2	no	—
73	C₄×Q₈×C₇₃	—	2	2	no	—
74	#117×C₇₃	D₄	1	1	yes	characteristic
75	Q₃₂×C₇₃	—	4	2	no	—
76	SD₃₂×C₇₃	—	4	2	no	—
77	SD₃₂×C₇₃	—	4	2	no	—
78	SD₃₂×C₇₃	—	4	2	no	—
79	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
80	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
81	#107×C₇₃	C₂³	1	2	yes	—
82	#106×C₇₃	—	2	1	no	—
83	#103×C₇₃	—	2	2	no	—
84	#103×C₇₃	—	2	2	no	—
85	#97×C₇₃	D₄	1	1	yes	characteristic
86	#97×C₇₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₂⁴×C₇₃	—	4	1	no	—
90	#41×C₇₃	—	4	2	no	—
91	#41×C₇₃	—	4	2	no	—
92	C₂×Q₈×C₇₃	—	2	2	no	—
93	C₂×Q₈×C₇₃	—	2	1	no	—
94	C₂×D₄×C₇₃	—	2	1	no	—
95	C₂×D₄×C₇₃	—	2	1	no	—
96	C₂×D₄×C₇₃	—	2	1	no	—
97	C₂×D₄×C₇₃	—	4	2	no	—
98	C₂×D₄×C₇₃	—	4	2	no	—
99	C₂×D₄×C₇₃	—	4	1	no	—
100	C₂×D₄×C₇₃	—	4	1	no	—
101	C₂×D₄×C₇₃	—	4	2	no	—
102	C₂×D₄×C₇₃	—	4	2	no	—
103	C₂²×C₄×C₇₃	—	4	1	no	—
104	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₇₃	—	2	2	no	—
106	Q₁₆×C₇₃	—	2	2	no	—
107	Q₁₆×C₇₃	—	2	2	no	—
108	Q₁₆×C₇₃	—	4	2	no	—
109	SD₁₆×C₇₃	—	4	2	no	—
110	SD₁₆×C₇₃	—	4	2	no	—
111	SD₁₆×C₇₃	—	4	2	no	—
112	D₈×C₇₃	—	2	2	no	—
113	D₈×C₇₃	—	2	2	no	—
114	D₈×C₇₃	—	2	2	no	—
115	D₈×C₇₃	—	4	2	no	—
116	D₈×C₇₃	—	4	2	no	—
117	D₈×C₇₃	—	4	2	no	—
118	M₁₆×C₇₃	—	2	2	no	—
119	C₂×C₈×C₇₃	—	2	2	no	—
120	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₇₃	—	2	2	no	—
125	C₄⋊C₄×C₇₃	—	4	2	no	—
126	C₄⋊C₄×C₇₃	—	4	2	no	—
127	C₄⋊C₄×C₇₃	—	4	2	no	—
128	C₄⋊C₄×C₇₃	—	4	2	no	—
129	C₄⋊C₄×C₇₃	D₈	1	2	yes	—
130	C₂²⋊C₄×C₇₃	—	4	2	no	—
131	C₂²⋊C₄×C₇₃	—	4	2	no	—
132	C₂²⋊C₄×C₇₃	—	4	2	no	—
133	C₂²⋊C₄×C₇₃	D₈	1	2	yes	—
134	C₄²×C₇₃	—	4	2	no	—
135	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₇₃	—	2	2	no	—
138	C₁₆×C₇₃	—	2	2	no	—
139	C₂³×C₇₃	—	4	1	no	—
140	C₂³×C₇₃	—	4	1	no	—
141	C₂³×C₇₃	—	4	1	no	—
142	C₂³×C₇₃	—	8	2	no	—
143	C₂³×C₇₃	—	16	2	no	—
144	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
145	Q₈×C₇₃	—	4	1	no	—
146	Q₈×C₇₃	—	4	2	no	—
147	Q₈×C₇₃	—	4	1	no	—
148	Q₈×C₇₃	—	4	2	no	—
149	D₄×C₇₃	—	4	1	no	—
150	D₄×C₇₃	—	4	1	no	—
151	D₄×C₇₃	—	4	1	no	—
152	D₄×C₇₃	—	4	1	no	—
153	D₄×C₇₃	—	4	1	no	—
154	D₄×C₇₃	—	4	1	no	—
155	D₄×C₇₃	—	8	2	no	—
156	D₄×C₇₃	—	8	2	no	—
157	D₄×C₇₃	—	16	2	no	—
158	D₄×C₇₃	—	16	2	no	—
159	C₂×C₄×C₇₃	—	2	1	no	—
160	C₂×C₄×C₇₃	—	2	1	no	—
161	C₂×C₄×C₇₃	—	4	2	no	—
162	C₂×C₄×C₇₃	—	4	2	no	—
163	C₂×C₄×C₇₃	—	4	1	no	—
164	C₂×C₄×C₇₃	—	8	2	no	—
165	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₇₃	—	2	1	no	—
170	C₈×C₇₃	—	2	1	no	—
171	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₈×C₇₃	H(5,𝔽₂)	1	2	yes	—
173	C₂²×C₇₃	—	2	2	no	—
174	C₂²×C₇₃	—	2	1	no	—
175	C₂²×C₇₃	—	8	2	no	—
176	C₂²×C₇₃	—	8	2	no	—
177	C₂²×C₇₃	—	8	2	no	—
178	C₂²×C₇₃	—	8	1	no	—
179	C₂²×C₇₃	—	8	1	no	—
180	C₂²×C₇₃	—	8	1	no	—
181	C₂²×C₇₃	—	16	4	no	—
182	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
183	C₄×C₇₃	—	2	2	no	—
184	C₄×C₇₃	—	2	2	no	—
185	C₄×C₇₃	—	2	1	no	—
186	C₄×C₇₃	—	8	2	no	—
187	C₄×C₇₃	—	8	1	no	—
188	C₄×C₇₃	—	8	2	no	—
189	C₄×C₇₃	#535	1	1	yes	characteristic
190	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	#33788	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₇₃	—	4	1	no	—
193	C₂×C₇₃	—	16	1	no	—
194	C₂×C₇₃	—	16	1	no	—
195	C₂×C₇₃	—	16	1	no	—
196	C₂×C₇₃	#3205	1	1	yes	characteristic
197	C₂×C₇₃	#3416	1	2	yes	—
198	#3177	C₂×C₇₃	1	1	yes	characteristic, complemented
199	#3155	C₂×C₇₃	1	1	yes	characteristic
200	#2251	C₂×C₇₃	1	1	yes	characteristic, complemented
201	#2248	C₂×C₇₃	1	1	yes	characteristic, complemented
202	#2244	C₂×C₇₃	1	1	yes	characteristic, complemented
203	#2242	C₂×C₇₃	1	1	yes	characteristic, complemented
204	#2211	C₂×C₇₃	1	2	yes	complemented
205	#2207	C₂×C₇₃	1	2	yes	complemented
206	#2189	C₂×C₇₃	1	2	yes	complemented
207	#2187	C₂×C₇₃	1	2	yes	complemented
208	#2164	C₂×C₇₃	1	1	yes	characteristic, complemented
209	C₇₃	#33788	1	1	yes	characteristic, direct product factor, Sylow
210	C₂×AGL(1,ℤ/8)	—	2	1	no	—
211	C₂×#135	C₂²×C₇₃	1	1	yes	characteristic
212	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
213	#541	—	2	1	no	—
214	#535	—	2	1	no	—
215	C₂×Q₃₂	C₂²×C₇₃	1	2	yes	complemented
216	C₂×SD₃₂	C₂²×C₇₃	1	2	yes	—
217	C₂×SD₃₂	C₂²×C₇₃	1	2	yes	—
218	C₂×SD₃₂	C₂²×C₇₃	1	2	yes	complemented
219	#499	C₂²×C₇₃	1	1	yes	characteristic, complemented
220	#496	—	2	1	no	—
221	#496	—	2	1	no	—
222	#495	C₂²×C₇₃	1	1	yes	characteristic
223	#495	C₂²×C₇₃	1	1	yes	characteristic
224	#494	C₂²×C₇₃	1	1	yes	characteristic, complemented
225	#493	C₂²×C₇₃	1	1	yes	characteristic
226	#493	C₂²×C₇₃	1	1	yes	characteristic
227	#491	—	2	1	no	—
228	#470	—	2	1	no	—
229	#467	C₂²×C₇₃	1	2	yes	—
230	#441	—	2	1	no	—
231	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
232	#405	C₂²×C₇₃	1	1	yes	characteristic
233	C₄⋊C₁₆	C₂²×C₇₃	1	2	yes	complemented
234	#358	C₂²×C₇₃	1	2	yes	complemented
235	#357	C₂²×C₇₃	1	2	yes	—
236	#357	C₂²×C₇₃	1	2	yes	—
237	#357	C₂²×C₇₃	1	2	yes	complemented
238	C₂²⋊C₁₆	C₂²×C₇₃	1	2	yes	—
239	#346	C₂²×C₇₃	1	1	yes	characteristic, complemented
240	C₄×C₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
241	C₂×#41	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	AGL(1,ℤ/8)	—	4	4	no	—
244	#135	—	4	2	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
247	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	4	2	no	—
255	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
256	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
257	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
258	C₂×M₁₆	D₄×C₇₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
260	C₄⋊Q₈	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#126	—	4	2	no	—
264	#125	—	2	1	no	—
265	#125	—	4	2	no	—
266	#124	—	2	1	no	—
267	#124	—	2	1	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	#121	—	4	2	no	—
270	#120	—	4	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	#117	D₄×C₇₃	1	1	yes	characteristic
273	Q₃₂	—	4	2	no	—
274	SD₃₂	—	4	2	no	—
275	SD₃₂	—	4	2	no	—
276	SD₃₂	—	4	2	no	—
277	C₂×C₁₆	C₂³×C₇₃	1	2	yes	—
278	C₂×C₁₆	C₂³×C₇₃	1	2	yes	—
279	#107	C₂³×C₇₃	1	2	yes	—
280	#106	—	2	1	no	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#97	D₄×C₇₃	1	1	yes	characteristic
284	#97	D₄×C₇₃	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
287	C₂⁴	—	4	1	no	—
288	#41	—	4	2	no	—
289	#41	—	4	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	2	2	no	—
306	Q₁₆	—	4	2	no	—
307	SD₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	SD₁₆	—	4	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	4	2	no	—
314	D₈	—	4	2	no	—
315	D₈	—	4	2	no	—
316	M₁₆	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
321	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	D₈×C₇₃	1	2	yes	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	D₈×C₇₃	1	2	yes	—
332	C₄²	—	4	2	no	—
333	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
335	C₁₆	—	2	2	no	—
336	C₁₆	—	2	2	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	16	2	no	—
342	C₂³	C₂×D₈×C₇₃	1	1	yes	characteristic
343	Q₈	—	4	1	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	2	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	16	2	no	—
356	D₄	—	16	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
364	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
365	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
370	C₈	H(5,𝔽₂)×C₇₃	1	2	yes	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	2	no	—
387	C₄	#535×C₇₃	1	1	yes	characteristic
388	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
389	C₂	—	4	1	no	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	—	16	1	no	—
393	C₂	C₇₃×#3205	1	1	yes	characteristic
394	C₂	C₇₃×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₃
prime radical	C₇₃×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #117×C₇₃ ◁ #405×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇₃×#3177	C₂	semidirect
3. C₇₃×#2251	C₂	semidirect
4. C₇₃×#2248	C₂	semidirect
5. C₇₃×#2244	C₂	semidirect
6. C₇₃×#2242	C₂	semidirect
7. C₇₃×#2211	C₂	semidirect
8. C₇₃×#2207	C₂	semidirect
9. C₇₃×#2189	C₂	semidirect
10. C₇₃×#2187	C₂	semidirect
11. C₇₃×#2164	C₂	semidirect
17. C₂×Q₃₂×C₇₃	C₂²	semidirect
20. C₂×SD₃₂×C₇₃	C₂²	semidirect
21. #499×C₇₃	C₂²	semidirect
26. #494×C₇₃	C₂²	semidirect
33. C₄×Q₁₆×C₇₃	C₂²	semidirect
35. C₄⋊C₁₆×C₇₃	C₂²	semidirect
36. #358×C₇₃	C₂²	semidirect
39. #357×C₇₃	C₂²	semidirect
41. #346×C₇₃	C₂²	semidirect
42. C₄×C₁₆×C₇₃	C₂²	semidirect
191. #33788	C₇₃	direct (N × H)
198. #3177	C₂×C₇₃	semidirect
200. #2251	C₂×C₇₃	semidirect
201. #2248	C₂×C₇₃	semidirect
202. #2244	C₂×C₇₃	semidirect
203. #2242	C₂×C₇₃	semidirect
204. #2211	C₂×C₇₃	semidirect
205. #2207	C₂×C₇₃	semidirect
206. #2189	C₂×C₇₃	semidirect
207. #2187	C₂×C₇₃	semidirect
208. #2164	C₂×C₇₃	semidirect
209. C₇₃	#33788	direct (N × H)
215. C₂×Q₃₂	C₂²×C₇₃	semidirect
218. C₂×SD₃₂	C₂²×C₇₃	semidirect
219. #499	C₂²×C₇₃	semidirect
224. #494	C₂²×C₇₃	semidirect
231. C₄×Q₁₆	C₂²×C₇₃	semidirect
233. C₄⋊C₁₆	C₂²×C₇₃	semidirect
234. #358	C₂²×C₇₃	semidirect
237. #357	C₂²×C₇₃	semidirect
239. #346	C₂²×C₇₃	semidirect
240. C₄×C₁₆	C₂²×C₇₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇₃×#3177	2
C₇₃×#3155	2
C₇₃×#2251	2
C₇₃×#2248	2
C₇₃×#2244	2
C₇₃×#2242	2
C₇₃×#2211	2
C₇₃×#2207	2
C₇₃×#2189	2
C₇₃×#2187	2
C₇₃×#2164	2
#33788	73

Subgroups — C73×#33788 #32943192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#33788 #32943192